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Special Issue: Lie Symmetry Analysis and Conservation Laws for Nonlinear Differential Equations and Applications

Guest Editors

Prof. M. L. Gandarias
Department of Mathematics, Faculty of Sciences, University of Cádiz, Puerto Real, Cádiz 11510, Spain
Email: marialuz.gandarias@uca.es


Prof. Rita Tracinà
Dipartimento di Matematica e Informatica, Università Degli Studi di Catania, Viale Andrea Doria, 6, Catania 95125, Italy
Email: tracina@dmi.unict.it


Prof. C. M. Khalique
International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X 2046, Mmabatho 2735, South Africa
Email: Masood.Khalique@nwu.ac.za

Manuscript Topics


Many real-world problems, which arise in various scientific fields such as economics, biology, fluid dynamics, physics, engineering, control theory, materials science, quantum mechanics, and in industry are modelled by physically and mathematically interesting nonlinear differential equations. Exact solutions of nonlinear differential equations graphically illustrate and provide us the mechanisms of many complex nonlinear phenomena. Exact solutions can also be used as “test problems” to establish the stability and estimate errors of many numerical and analytical methods.


Over the past years, several methods have been developed to construct exact solutions of such nonlinear differential equations. However, Lie symmetry analysis is a powerful and effective tool which can produce exact solutions of nonlinear differential equations. The aim of this special issue will be to report on recent developments in Lie symmetry analysis and conservation laws for solving such nonlinear differential equations as well as their new applications in several fields of natural sciences and engineering. We are interested in high-quality papers that contain original research results.


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Paper Submission

All manuscripts will be peer-reviewed before their acceptance for publication. The deadline for manuscript submission is 30 June 2024

Published Papers(11)

Research article
Solutions of initial and boundary value problems using invariant curves
Khudija Bibi
2024, Volume 9, Issue 8: 22057-22066. doi: 10.3934/math.20241072
Abstract HTML PDF Viewed (1048)
Research article
Unveiling solitons and dynamic patterns for a (3+1)-dimensional model describing nonlinear wave motion
Muhammad Bilal Riaz Syeda Sarwat Kazmi Adil Jhangeer Jan Martinovic
2024, Volume 9, Issue 8: 20390-20412. doi: 10.3934/math.2024992
Abstract HTML PDF Cited (3) Viewed (1147)
Research article
Application of symmetry analysis and conservation laws to a fractional-order nonlinear conduction-diffusion model
A. Tomar H. Kumar M. Ali H. Gandhi D. Singh G. Pathak
2024, Volume 9, Issue 7: 17154-17170. doi: 10.3934/math.2024833
Abstract HTML PDF Viewed (1284)
Research article
Symmetry reductions and conservation laws of a modified-mixed KdV equation: exploring new interaction solutions
Nauman Raza Maria Luz Gandarias Ghada Ali Basendwah
2024, Volume 9, Issue 4: 10289-10303. doi: 10.3934/math.2024503
Abstract HTML PDF Cited (2) Viewed (1217)
Research article
The invariant solution with blow-up for the gas dynamics equations from one-parameter three-dimensional subalgebra consisting of space, Galilean and pressure translations
Dilara Siraeva
2024, Volume 9, Issue 1: 89-98. doi: 10.3934/math.2024006
Abstract HTML PDF Viewed (1581)
Research article
Symmetry analysis and conservation laws of time fractional Airy type and other KdV type equations
Miguel Vivas-Cortez Yasir Masood Absar Ul Haq Imran Abbas Baloch Abdul Hamid Kara F. D. Zaman
2023, Volume 8, Issue 12: 29569-29576. doi: 10.3934/math.20231514
Abstract HTML PDF Cited (1) Viewed (1566)
Research article
Conservation laws and symmetry analysis of a generalized Drinfeld-Sokolov system
Tamara M. Garrido Rafael de la Rosa Elena Recio Almudena P. Márquez
2023, Volume 8, Issue 12: 28628-28645. doi: 10.3934/math.20231465
Abstract HTML PDF Viewed (1473)
Research article
Study on the symmetries and conserved quantities of flexible mechanical multibody dynamics
Mingliang Zheng
2023, Volume 8, Issue 11: 27969-27982. doi: 10.3934/math.20231430
Abstract HTML PDF Viewed (1383)
Research article
The mR scheme to the shallow water equation with horizontal density gradients in one and two dimensions
Kamel Mohamed H. S. Alayachi Mahmoud A. E. Abdelrahman
2023, Volume 8, Issue 11: 25754-25771. doi: 10.3934/math.20231314
Abstract HTML PDF Cited (3) Viewed (2011)
Research article
Exact solutions and superposition rules for Hamiltonian systems generalizing time-dependent SIS epidemic models with stochastic fluctuations
Rutwig Campoamor-Stursberg Eduardo Fernández-Saiz Francisco J. Herranz
2023, Volume 8, Issue 10: 24025-24052. doi: 10.3934/math.20231225
Abstract HTML PDF Cited (4) Viewed (1640)
Research article
Analytical solutions for nonlinear systems using Nucci's reduction approach and generalized projective Riccati equations
Huitzilin Yépez-Martínez Mir Sajjad Hashemi Ali Saleh Alshomrani Mustafa Inc
2023, Volume 8, Issue 7: 16655-16690. doi: 10.3934/math.2023852
Abstract HTML PDF Cited (8) Viewed (2062)